Solve for $x$ and $y$ using elimination. ${-3x+3y = 18}$ ${-2x-4y = -48}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $-3$ ${-6x+6y = 36}$ $6x+12y = 144$ Add the top and bottom equations together. $18y = 180$ $\dfrac{18y}{{18}} = \dfrac{180}{{18}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x+3y = 18}\thinspace$ to find $x$ ${-3x + 3}{(10)}{= 18}$ $-3x+30 = 18$ $-3x+30{-30} = 18{-30}$ $-3x = -12$ $\dfrac{-3x}{{-3}} = \dfrac{-12}{{-3}}$ ${x = 4}$ You can also plug ${y = 10}$ into $\thinspace {-2x-4y = -48}\thinspace$ and get the same answer for $x$ : ${-2x - 4}{(10)}{= -48}$ ${x = 4}$